ONE CODIMENSIONAL WECKEN TYPE THEOREMS

We generalize the results of [DG] onto the pairs of maps f, g: M --> N between smooth manifolds satisfying dim M = dim N + 1 greater-than-or -equal-to 5. We consider Nielsen classes of the coincidence set of the pair f, g and define for them two conditions W1 and W2. Any class whi ch does not satisfy any of these conditions can not disappear during a ny homotopy. We give also some condition when W1 and W2 are the only o bstructions to remove a Nielsen class.